1. Microwave Cooking Modeling Heat and moisture transport Andriy Rychahivskyy

2. Outline What is a microwave? Nature of microwave heating Goals of the project Model description Results Conclusions and recommendations

3. Scheme of a microwave oven

4.  H ─electric field ─ electric field ─ magnetic field ─ wavelength (12.2 cm for 2.45 GHz)  H What is a microwave?

5. Microwave cooking principle Microwaves act on salt ions 1) salt ions to accelerate them; water molecules 2) water molecules to rapidly change their polar direction + + 

6. Microwave cooking principle Microwaves act on salt ions 1) salt ions to accelerate them; water molecules 2) water molecules to rapidly change their polar direction Food’s water content heats the food due to molecular “friction”

7. Goal of the project Design a model of microwave cooking predicting temperature and moisture distribution within the food product

8. Phenomena to model Electromagnetic wave distribution Heat transport within the product Mass (water and vapor) transport

9. Governing equations and laws Maxwell’s equations Energy balance equation Water and vapor balance equations Ideal gas law Darcy’s law for a flow in a porous medium

10. Porous medium water vapor solid particle

11. Porous medium water vapor solid particle

12. Geometrical model MW cavity C ­ MW cavity food product M ­ food product waveguide G ­ waveguide top bottom

13. Heat source –electromagnetic properties: ε, σ –electromagnetic properties: ε, σ (control how a material heats up) ε = ε* + i ε** –radial frequency: ω = 2  *2.45 GHz

14. Heat source Electric field intensity

15. Heat source Electric field intensity

16. Heat source Electric field intensity Heat source

17. Convection-diffusion equation heat capacity : heat capacity : (how much heat the food holds) thermal conductivity: (how fast heat moves) latent heat: (absorbed due to evaporation) interface mass transfer rate:

18. Boundary and initial conditions thermal conductivity: (how fast heat moves) heat transfer coef.: (thermal resistance) latent heat: (absorbed due to evaporation)

19. One-dimensional model with at

20. Numerical results /without mass transport/

22. Numerical results /general 1D model/

23. Interpretation of results

24. Conclusions Electromagnetic source is constant Heating-up of the product until 100 o C develops linear in time T at the boundary >> T in the kernel Moisture loss occurs only in a boundary layer

25. Recommendations Validate the results Extend our implementation Perform a parameter study